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World desk7 min

How to Measure Thiele–Small Parameters for a Loudspeaker Driver

A free-air impedance sweep is the starting point for measuring Thiele–Small parameters. Learn when you need added mass, a known moving mass, or a test box—and how to keep the measurement useful.

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Start with a low-level free-air impedance sweep, then supply the extra information needed to calculate parameters such as Vas: a known moving mass, a carefully measured added mass and resonance shift, or a test box of known volume. The best method depends on what you can measure reliably. For most DIY measurements, the classic added-mass method is a practical choice; a three-sweep dual-added-mass fit offers more diagnostics but requires careful weighing and setup.

What a free-air impedance sweep can—and cannot—tell you

A free-air impedance sweep is the starting point: it measures the driver’s electrical impedance across frequency while the diaphragm is not loaded by an enclosure. An analyzer can use the curve to report resonance frequency (Fs), voice-coil DC resistance (Re), inductance, and total Q. The sweep alone does not establish every Thiele–Small parameter. To derive values such as Vas, Bl, or moving mass, the method also needs a known moving mass, a known added mass and the resulting resonance change, or a test box with a known volume.

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Thiele–Small parameters describe a driver’s small-signal behavior and are used to model enclosure performance. They are useful only in context: measurement method, drive level, mounting, and conditioning can affect comparisons. Treat the result as a measurement under recorded conditions, not as a context-free property.

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Choose a measurement method

Method What you need What it adds Trade-offs
Known moving mass (Mms) A free-air sweep and a credible Mms value that matches the software’s definition Lets software derive additional parameters from the free-air measurement No added-mass operation or test box, but supplied or measured mass must be compatible with the software’s definition and conditions.
Classic added mass Free-air sweeps before and after applying a known mass; a scale and removable, evenly distributed weights Uses the resonance shift to calculate additional parameters, including Vas Avoids a test box; mass accuracy and stable placement matter. In the reviewed DATS LA workflow, a resonance shift below 25% is flagged as too small.
Known-volume test box A free-air measurement and a test box with known volume Provides an alternative route to the remaining parameters Requires a suitable box and volume measurement. The reviewed material does not establish a universal box-sizing or sealing procedure; account for the driver’s own volume when determining the effective volume.
Dual-added-mass fit Three impedance measurements, four small masses, accurate weighing, and software that fits the model and reports diagnostics Fits an advanced small-signal model and provides fit-quality information More steps than the classic method, but includes quality ratings and diagnostic plots. The method’s authors report Bl within 1.0% and Mms within 2% for their procedure; these are author-reported results, not an independent comparison.
Specified SPL Not stated in the reviewed material Included as a Vas approach in a method comparison There is not enough procedural detail here to describe a complete SPL-based measurement.

For an initial DIY measurement, the classic added-mass method is a reasonable route if you can weigh and place the mass carefully. Prefer the dual-added-mass approach when you want its additional model fit and diagnostics and can follow the three-measurement procedure. Choose a test box when you can establish its effective volume and seal the setup reliably.

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Prepare the driver and analyzer

  1. Secure the frame. Clamp or fixture the driver so the frame cannot move while leaving the diaphragm free. In an audioXpress review of the Dayton Audio DATS LA, the reviewer said a vise could suffice for small-signal measurements, but frame flex may appear at higher drive levels; for serious higher-level work, the reviewer recommended securing the frame at multiple points. Avoid a fixture that presses on or obstructs the cone.
  2. Select a low sweep level and suitable frequency range. The same reviewer used the DATS LA default setting of -10 dBU (0.245 Vrms) and a 5 Hz to 5 kHz range for woofers. That is one example, not a universal standard: use settings suitable for your driver and analyzer, and keep the measurement in the small-signal region.
  3. Measure and save the free-air impedance curve. Keep the diaphragm unloaded and at rest. Record the analyzer’s reported values and retain the curve if the software allows it; the curve helps assess whether the resonance is clear and the measurement is repeatable.
  4. Record the conditions. Note the sweep level, frequency range, fixture, added mass or box configuration, and whether the driver was preconditioned. Those details are necessary to interpret later comparisons.

Use the classic added-mass method

Measure the free-air baseline

With the driver secured and the cone free, run and save the first impedance sweep. This provides the unweighted resonance needed for comparison. Do not change the fixture or sweep settings between the baseline and weighted measurement.

Add and weigh mass

Use a known mass that produces a sufficiently clear resonance shift. The reviewed DATS LA procedure warns when the shift is less than 25% and calls for more weight. That threshold is specific to the described workflow, not a universal requirement for all analyzers or methods. Weigh the total added mass rather than relying on nominal labels.

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Distribute the mass evenly near the voice coil so the cone does not tilt or rock. Attach it securely without damaging the diaphragm, and check that the cone’s resting position has not been disturbed. Uneven loading can undermine the resonance comparison.

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Run the weighted sweep and calculate

Repeat the impedance sweep using the same level, range, fixture, and analyzer settings. Enter the measured mass and the weighted and unweighted resonance results into the analyzer or software’s added-mass workflow. Follow the software’s definitions and prompts; the available sources do not provide a universal equation set that applies identically across implementations.

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If the resonance shift is too small for the software’s method, add more mass evenly and repeat the weighted measurement. If the curve is unstable or the cone moves off-center, correct the setup before trusting the calculated values.

Run the three-measurement dual-added-mass procedure

The dual-added-mass method described by Claus Futtrup and Jeff Candy (2021) uses three impedance measurements and an advanced model fit:

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  1. Attach four small masses. Distribute them evenly around the cone and measure impedance with all four attached.
  2. Remove two diagonal masses. Keep the cone at rest while removing them, then measure impedance again with the remaining pair in place.
  3. Remove the remaining masses. Measure impedance a third time with the cone unweighted.
  4. Weigh the removed portions accurately. Record the actual mass represented by each state and enter the measurements and mass values into the fitting software.

Speakerbench recommends 0.1 g weighing precision for normal transducers with Mms of 10–25 g. That is a recommendation for the stated mass range, not a universal precision specification for every driver. The software fits the measurements and supplies quality ratings and diagnostic plots; its authors describe the fit as a small-signal model and say a “good” fit is sufficient for reasonably accurate box simulations. Inspect the diagnostics rather than treating a numerical output as proof of a sound setup.

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Use a known-volume test box or known Mms

Known-volume box

A known-volume test box is an alternative to adding mass. Its useful volume must be established accurately, including adjustment for the volume displaced by the driver itself. Then take the measurements and enter the box volume according to the analyzer or software’s procedure. The reviewed sources do not give a universal box size, construction, or sealing protocol, so follow the specific analyzer’s documentation rather than assuming one box design works for every driver.

Specified moving mass

Some software accepts a supplied Mms and uses it with a free-air sweep to calculate further parameters. Before entering a datasheet value, confirm that it means the same quantity and was determined under compatible conditions. The available sources do not establish a general conversion or equivalence rule between all reported Mmd and Mms values.

Check the result and compare it fairly

  • Review the curve and fit. A clear resonance and a satisfactory software fit are more useful than a list of outputs without diagnostics. For the dual-added-mass approach, use the supplied quality rating and plots.
  • Repeat if the setup changed. A shifted fixture, disturbed cone, tilted added mass, or inconsistent sweep settings can make a comparison unreliable.
  • Compare like with like. Different Vas methods can give different displayed values. A comparison of test-box, added-mass, specified-SPL, and specified-Mmd approaches showed method-dependent results; a difference alone does not prove that either value is wrong.
  • Read the manufacturer’s conditions. Tymphany’s Peerless product sheet, printed March 2024, says its parameters were measured in free air without preconditioning and may therefore show deviation. It also notes that impedance and Fs may be measured under different conditions. The sheet states: “Details on this spec sheet are for reference only and should not be used for setting production limits.” Check such qualifications before comparing a datasheet with your own measurement.

An audioXpress reviewer reported that the DATS LA example measurements were close to results from two other systems. That is the reviewer’s experience with the tested setup and samples, not a guarantee that different analyzers or measurement conditions will agree.

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What to include in your measurement notes

  • Driver identity and whether it was preconditioned.
  • Fixture and whether the frame was secured at multiple points.
  • Analyzer, sweep frequency range, and drive level.
  • Method used: known Mms, classic added mass, dual-added-mass fit, or test box.
  • Actual mass values and placement, or the test box’s effective volume.
  • Reported parameter values plus the impedance curve and any fit-quality diagnostics.

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